A NEW YORK CITY school employee forged a daughter’s death certificate to get extra vacation time in Costa Rica and has since been fired, according to a report by the school system.

Joan Barnett, 58, a parent coordinator at the High School of Hospitality and Management, submitted an altered death certificate to get approved leave time in March and April 2010, according to the report by the Commissioner of Investigation. She lost her job that June after the forgery came to light.

It was first reported yesterday in the Daily News of New York. According to the report, someone who said she was Barnett’s daughter called the school on March 19, 2010, and said her sister in Costa Rica was very sick.

Later that day, the report said, another supposed daughter of Barnett’s called and said her sister had suffered a heart attack and died. She said relatives were gathering in Costa Rica.

Barnett faxed the school a death certificate April 8, the report said.

School officials were suspicious because it had different, misaligned fonts. A Costa Rican government official later confirmed the document was a fake, noting that the death certificate had been issued in 2005.

In addition to losing her job, Barnett pleaded guilty to a misdemeanor forgery charge last fall and was sentenced to 10 days’ community service. Her attorney did not return a call seeking comment yesterday.

Neither the criminal complaint against Barnett nor the special commissioner’s report addresses the question of whether the daughter who purportedly died ever existed.

Laurel Wright-Hinckson, a spokeswoman for the special commissioner’s office, said that Barnett refused to speak to investigators, who were “unable to ascertain if in fact she had said daughter and if she did, if this daughter did pass away.”